3818A generalization of Pascal theorem and Pappus theorem
- Jun 18, 2017
Dear Dr. Paul Yiu, and Geometers,
Let 1, 2, 3, 4, 5, 6 be six arbitrary points in a hyperbola. Let 1' be arbitrary point in the hyperbola. The circle (121') meets the hyperbola at point 2'. The circle (232) meets the hyperbola again at 3', define points 4', 5', 6' similarly. Let circle (121') meets the circle (454') at A, B, Let circle (232') meets the circle (565') at C, D. Let circle (343') meets the circle (616') at E, F. Then six points A, B, C, D, E, F lie on a circle.
1. If 1' at \infty the theorem is Pascal theorem
2. If the hyperbola is two lines, and 1' at \infty the theorem is Pappus theorem
Dao Thanh Oai